Answer
$x-2y=-13$
Work Step by Step
Using $y-y_1=m(x-x_1)$ or the point-slope form of linear equations, the equation of the line passing through $(
-5,4
)$ and with a slope of $m=
\dfrac{1}{2}
$ is
\begin{array}{l}\require{cancel}
y-4=\dfrac{1}{2}(x-(-5))
\\\\
y-4=\dfrac{1}{2}(x+5)
.\end{array}
In the form $y=mx+b$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y-4=\dfrac{1}{2}(x+5)
\\\\
y-4=\dfrac{1}{2}x+\dfrac{5}{2}
\\\\
y=\dfrac{1}{2}x+\dfrac{5}{2}+4
\\\\
y=\dfrac{1}{2}x+\dfrac{5}{2}+\dfrac{8}{2}
\\\\
y=\dfrac{1}{2}x+\dfrac{13}{2}
.\end{array}
In the form $Ax+By=C$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y=\dfrac{1}{2}x+\dfrac{13}{2}
\\\\
2(y)=2\left( \dfrac{1}{2}x+\dfrac{13}{2} \right)
\\\\
2y=x+13
\\\\
-x+2y=13
\\\\
x-2y=-13
.\end{array}
Hence, the different forms of the equation of the line with the given conditions are
\begin{array}{l}\require{cancel}
\text{slope-intercept form: }
y=\dfrac{1}{2}x+\dfrac{13}{2}
\\\\
\text{standard form: }
x-2y=-13
.\end{array}
